Efficient Spectrum Allocation Using Case-Based

Efficient Spectrum Allocation Using Case-Based Reasoning and Collaborative Filtering Approaches

Yenumula B. Reddy Grambling State University, LA 71245, USA [email protected]

Abstract — Cognitive radio environments utilize the scarce resource like spectrum efficiently through the dynamic spectrum access approach. Various models, including economic, game theory, genetic algorithms, and neural network models will become the catalysts to boost the dynamic spectrum access for efficient utilization of the spectrum. Combinations of these models may sometimes help better in allocation of unused spectrum (spectrum holes) for cognitive users (secondary users). In this paper, we introduced the case-base reasoning to identify a channel preferred by the secondary user. We then introduced automatic collaborative filtering for preference between two users which assigns the particular channel to the highest prioritized user. These two approaches were used along with the cooperative game concept to select the preferred channel for a cognitive user at any given time slot. The framework was designed using the CBR-ACF Algorithm and discussed using examples generated through simulations. Keywords-dynamic spectrum access; spectrum holes; casebased reasoning; automatic collaborative filtering; cooperative games.

1. INTRODUCTION The existing problem for static allocation of the spectrum is a major hurdle for its efficient utilization. Recent research concentrates on efficient allocation of the current allotted spectrum without disturbing the licensed users [1-3]. For efficient allocation of the unused spectrum, one must create algorithms to track the spectrum at any given time and location and allocate to the needed users. The design requires appropriate detectors at the physical layer for sensing and accessing the strategies at the MAC layer. If the traffic on the communication space is random, the fixed channel allocation method is inefficient. Thus a randomized dynamic sensing policy is needed for allocation of the channels to the most qualified user (s) while avoiding other competing users. The randomized dynamic policy related to spectrum allocation uses the unused spectrum (spectrum holes) of primary users (PU). The secondary users (cognitive users) adopt several methodologies to identify spectrum holes, learn from current communication environment, and exploit the opportunities to grab the spectrum without disturbing the primary user. This means that the cognitive users can create flexible access to the spectrum. They can partition the spectrum into a large number of orthogonal channels and complete the transmission simultaneously with a flexible set of channels. To do such a partition we must design a distributed approach for dynamic spectrum access. The approach may use graph models, game theory models, or any other Artificial Intelligence related models that quickly adapt to the varying traffic demands. These

models determine the number of channels to use and maximize user throughput. These strategies follow the local maxima and continue until they achieve global maxima. To use the spectrum holes efficiently, we must create the spectrum sharing scenario where multiple secondary users (SUs) coexist in the same area and communicate with the same portion of the spectrum. For efficient utilization of the spectrum holes, the game models are proposed in a multi-user environment because they were tested in a share market (particularly in auction related problems) and introduced recently in wireless communications [4-8]. The spectrum sharing problem can be solved with the cooperation of economic models and the selfish motivation of game models. In cooperative and selfish environments the SU must consider the presence of other SUs as well as primary users (PUs). In a cooperative environment it is required to consider explicit communication between SUs [9] only. In the selfish environment, the SUs compete for the resources using machine learning models or game models [1, 10, 11]. In recent years, the FCC has been promoting the technologies for the efficient utilization of the spectrum. The FCC’s interest helped industries to introduce devices with various capabilities including frequency agility, adaptive modulation, transmit power control, and localization. Furthermore, the NeXT generation program of the Defense Advanced Research Program Agency (DARPA) concentrated on technology based on using cognitive radios (CR) for efficient utilization of the spectrum. Therefore, dynamic spectrum access (DSA) became a promising approach for efficient utilization of the spectrum [12]. The key component for DSA is the sharing the spectrum with efficient allocation of the unused spectrum resources and the scheduling these resources among the SUs. Identification of the unused spectrum is the main part of the resource allocation. CRs play a major role in sensing unused spectrum intelligently making the appropriate decisions to gain access to unused spectrum. Game models help to select the unused spectrum intelligently and bring above the appropriate outcome for efficient allocation of resources. Since multiple users are involved in the process, security becomes an important factor. Therefore, CRs have additional work to deal with selfish and malicious users. In this research, case-based reasoning and automatic collaborative filtering concepts were used to allocate the preferred channel to the SU. The concept of the cooperative game approach boosts the case-based reasoning and automatic filtering models in maximizing channel allocation to a prioritized SU.

The Contribution The contribution includes the design of the problem with opportunistic access to the spectrum for secondary users at any given time slot and formulating the problem as a game. The reward and penalty for user action is introduced depending upon the channel gain by the SU. The problem solution is dealt with game model using the collaborative effort of SUs. The collaborative effort of SUs is combined with case-based reasoning and automatic collaborating filtering to gain a preferred channel by a SU. The channel gain by SUs was explained using Algorithm CBR-ACF. The algorithm was discussed using simulations with random data developed in the MATLAB language. The rest of the paper is organized as follows: The related work and recent developments are discussed in section 2. The formulation of the problem and role of game models in DSA are introduced in section 3. Section 4 introduces the case-based reasoning and automatic collaborating filtering. Sections 5 and 6 discuss the cooperative game model and preference of a channel for secondary users. Section 7 provides the algorithm and simulations using examples with sample data and section 8 concludes the results and outlines the future research. 2. RELATED WORK The overview of the opportunistic spectrum access and taxonomy of dynamic spectrum access was provided by Zhao et al. [13]. This paper [13] helps to eliminate the confusion of the broad term CR as a synonym for dynamic spectrum access (DSA) and provides the clear distinction between the spectrum property rights, dynamic spectrum allocation, ultra wide band (spectrum underlay) and opportunistic spectrum access (spectrum overlay). The recent developments for efficient utilization of spectrum holes include the role of cognitive radio using economic, game, stochastic, and Markov decision process models [14-18]. Xie [7] discussed the overlay cognitive radio market model. In the model discussed by Xie, the primary user imposes the spectral mask so that the secondary user gets better spectrum use opportunities. Furthermore, for efficient usage of unused spectrum, the primary user uses the economics competition for purchase of power allocation on each channel. This economic model uses the market equilibrium while controlling the interferences. The real-time spectrum auctions discussed by Gandhi et al. [19] include spectrum bidding behaviors and pricing models. The model discusses the spectrum demands and how to maximize the revenue for efficient utilization of the spectrum. The auction-based dynamic spectrum allocation to lease the spectrum by secondary users was discussed by Wu [8]. In their paper, they proposed a mechanism called “multi-winner spectrum auction with a collision resistant pricing strategy” to allocate the spectrum optimally. The greedy algorithm proposed by Wu helps to reduce the complexity in multi-band auctions. The game models for spectrum sharing and controlled interference is studied in [9, 20 -22]. Nie et al. [20] formulated the channel allocation as a potential game and showed the improvement of the overall network performance. Ji et al. [21] discussed the dynamic spectrum sharing through the game theory approach and discussed the analysis of the networks, the user’s behavior, and the

optimal analysis of the spectrum unused allocation. Halldorsson et al. [22] viewed channel assignment as a game and provided the price anarchy depending upon the assumptions of the underlying network. Finally, Liu et al. [9] used the congestion game model for spectrum sharing and base station channel adaptation. In the current research, we introduced the opportunistic channel access by secondary users represented by a tuple consisting of number of users contesting, the resources available, and the strategies used by the users that create an objective function (utility function). Whenever a user tries to gain an action to a channel, three cases arise. The user request is often accepted, denied, and user has no action. If user has no action then there is no reward or penalty. In other cases, if the user request was accepted then the user will be rewarded else penalized. We further introduced the cooperative way of gaining a channel using case-based reasoning (CBR) or automatic collaborative filtering (ACF) or combination of these models. These two models help to gain the channel access with the help of user’s previous experience which includes channel weight and channel rating. The preference is calculated using nearest neighbor algorithm and/or mean square difference formula. These two formulas were used with users’ cooperation activity. The cooperative activity includes their channels rating and user preferences. Using these concepts, the SU demands will be fulfilled. 3. FORMULATION OF THE PROBLEM Let P denote the primary user (PU) and S denote the secondary users (SU). There are N primary users and M secondary users. Each primary user Pi (i = 1...N ) has

Bi ( i = 1, ... , N ) and secondary user S i (i = 1...M ) that competes with other secondary bandwidth

users to gain access to unused spectrum by PUs. The SU or cognitive users (CU) compete for the spectrum during sleeping time (unused time) of PU. The available spectrum slots depend upon the geographical locations. Depending upon the geographical location, the secondary user S i may be in the range of a different set of PUs and each SU competes for spectrum and sense it at the beginning of each time slot. th The availability of j primary channel ( j = 1...N ) for i secondary user (i = 1...M ) depends upon the probability of the channel availability and the opportunistic th access by the i SU. Suppose, there are κ primary channels available to M secondary users competing at any given time slot t , then each SU has the chance of obtaining the channel at a time slot t is κ / M . Therefore, th

the opportunity for the i SU to access the κ available primary channels at any time slot t is S ik (t ) = κ / Μ = K , for i ∈ M . th

The total opportunities for all secondary users at any time slot for κ available primary channels is M

M

i =1

i =1

∑ Sik (t ) =∑ K i (t ) and t ∈ T the time unit.

The opportunistic channel access is represented by the tuple ( S , Κ , Π , U ) , where S is the set of SUs competing for resources Κ ( k i ∈ Κ ) which is a set of channels available to SU at any given time slot t , and each SU uses the strategy π ∈ Π that generates the utility u ∈ U . For each action of the secondary user S i , the user senses the spectrum with a strategy

π i . The sensing action may get

success/fail with reward Ri which is 1 or -1. The channel access tuple can be represented as a game, where each SU in the game uses a strategy to compete for the resource called spectrum that costs for gaining the specific utility as the object function. During the process the SU may gain or lose the opportunity and generate the reward or penalty. Therefore, the game model G is represented as

G = {S , Κ , Π, U }

T

ℜ = Λ ∑∑ Rit

(2)

i =1 t =1

and Λ is a constant 0 ≤ Λ ≤ 1 . 1 if user i gains resource with strategyπ i at time slot t

Rit = 0

for no action

similarity function sim , input case of retrieval case of

(3)

− 1 if user i fails to obtain the resource at time slot t

The sensing policy of the cognitive user decides the action to be taken at a given time slot. Once the channel is sensed as free then the allocation policy decides which secondary user has priority to gain the access. The average reward per time slot ( T ) is calculated as ℜ / T and will be used for throughput criteria. The channel gained by the SU depends upon the current state and policy of the assignment that maximizes the total reward. Therefore, the channel assignment to the SU depends upon probability of availability of a channel and the probability of getting a channel. The probability of availability of a channel to a SU at any time slot t is κ / M and the probability of assignment of channel will be obtained by using the case-based reasoning (CBR) policy [23, 24]. 4. CASE-BASED REASONING AND AUTOMATIC COLLABORATIVE FILTERING In the selection of a product, CBR is used when experts find it hard to articulate their thought processes because the knowledge acquisition for these cases would be extremely difficult in such domains and is likely to produce incomplete or inaccurate results. CBR systems allow the case-base to establish characterized cases incrementally. Therefore, the case of SU is established incrementally for priority policy. A widely used formula for CBR in identifying and recommending similar channels (spectrum) is the nearest neighbor retrieval, which is based on weighted Euclidean distance [23].

i th feature f i I , and

i th feature f i R is given by ( Φ ) [24]: n

Φ=

(1)

The total benefits are the sum of all gains minus the sum of all penalties. Therefore, the total reward ℜ is given by M

The nearest neighbor algorithm deals with the similarity between the priority of stored cases and new available channel based on matching a weighted sum of features. The toughest problem is to determine the weights of the features. The limitation of this approach includes problems in converging on the correct solution and retrieval times. A typical algorithm for calculating nearest neighbor matching is the one used by Cognitive Systems Remind software reported in Kolodner [24]. The nearest th neighbor algorithm with weight of a i feature ( wi ),

∑ w × sim( f i =1

i

I i

, fiR ) ( 4)

n

∑w i =1

i

Equation (4) calculates the nearest neighbor of the best channel from the available channels of SU. If the th th difference between the i and j feature is negligibly smaller than the two features are closely matched. Equation (4) calculates the highly rated and close matching th interests of the i user channel. The selection will be compared with ACF. The final selection will be the combined result of ACF and CBR. Automated collaborated filtering (ACF) is a recommendation of a product based on word of mouth. In ACF, if user A’s ratings of a channel (or channels) matches with another user B’s ratings then it is possible to predict the ratings of a new channel for A, if B’s rating for that channel is available. In other words, let us assume that if users X, Y, and Z have common interest in the channels C1, C2, and C3, then if X, Y did high rate of channel C4, then we can recommend the C4 for Z. That is, we can predict that user Z bids high for that channel C4, since C4 is close interest of Z. The approximate bid of a kth bidder can be calculated by storing the bids of current bidders on the spectrum. The ACF uses the mean squared difference formula [25] with two users. Let U and J be two SUs interested in a channel. Let U f and J f be the ratings of U and J on a

f of the channel. Let χ be the set of features of the channel. Both U and J are rated and f ∈ χ . The difference between two persons U and J in terms of their feature

interests on a channel is given by [25]:

∆ = δU , J =

1 |χ|

∑ (U f ∈S

f

− J f )2

(5)

Two types of ACF recommendations, invasive and non-invasive based on the user preferences [26, 27]. An invasive approach requires explicit user feedback, where the preferences can vary between 0 and 1. In the noninvasive approach, the preferences are interactive and Boolean values. In the non-invasive rating 0 means the user not rated and 1 means rated. Therefore in noninvasive cases, it requires more data for any decision. In

ACF systems all user recommendations will be taken into account, even though they are entered at different times. More user recommendations provide good strength for the ACF recommendation system and the new recommendations solely depends upon the data. 5. COOPERATIVE GAME MODEL In cooperative games, the competition between coalitions of players groups the players and enforces cooperative behavior. The players choose the strategies by a consensus decision making process. In cooperative games it is assumed that each player has more than one choice, the combination of choices may win/loose/draw with an assigned payoff, players know the rules, and the player will select the higher payoff. The payoff will be as in equation (3) and the channel selection will be as per equations (4) and (5). That is, the channel selection will be done using the CBR and/or ACF procedure using the cooperative behavior of the players. The assignment of the channel to SU will depend upon the characteristic function ν as defined below:

6. PREFERENCE OF THE CHANNEL Let us assume that there are four SUs, rated using eight channels that were used before. The weights are the user ratings and the preferences are the similarity function sim . The sim is based on availability and retrieval (preference). Let the preference selection rate vary as 0 ≤ sim ≤ 1 . Similarly, the user rating (weight) also varies 0 ≤ wi ≤ 1 . The preference of a channel is calculated with randomly selected values as in Table I. The Table 1 uses the abbreviations as below: U# = User number C# = Channel Number CR = Channel Rating CRR = Channel Retrieval Rate w = weight assigned to channel sim = Average weight TABLE I: SPECTRUM BIDDING WITH N CHANNELS AND K USERS

Definition 1: The tuple ( M ,ν ) is a cooperative game only ifν is monotone. This concludes that the cost assignment is positive. That is, ν ( S ) ≤ ν ( S ) for all S '

⊆S ⊆M.

related to a channel, then the allocation is efficient if xi is inν (S ) . That is

∑x i =1

i

C#

CR

CRR

1

1

0.5

0.6

2 1 4 3 2 1 2

2 4 3 5 8 7 6

0.4 0.6 0.8 0.2 0.5 0.8 0.6

0.4 0.5 0.7 0.3 0.6 0.8 0.6

sim 0.55

w 0.6

'

Using the definition 1 and equations (4) and (5), the channel preferences can be arranged monotonically, so that the SU will get the best choice from the available channels. For example, let us consider the similar interest SUs into a sub group S ' where S ' ⊆ S . The similar interest SUs on a particular available channel needs the priority of these users. The best available channel that will be calculated using equation (4) and equation (5) then provide the difference between two users in terms of their interest. Therefore, it is easy to assign the closely matching channel to one of the SU. In a cooperative game an allocation is simply a overall value created and received by a particular user. For example if xi for i = 1,2,3...n , a collection of values n

U#

=ν ( S ) .

This shows that each player (SU) must get as much as they need without interacting with other users. The creation of quantity ν (S ) means the efficiency of its created values and gain of access to the appropriate channel by a SU. Definition 2: The marginal contribution of a player is the amount by which the overall value created would shrink if that player has to leave the game. This definition clearly explains that in a collaborative effort, marginal contribution members deduce something about the overall contribution to a particular game. This is one justification for a cooperative game related to users’ contribution and leads towards the justification of channel selection.

0.4 0.55 0.75 0.25 0.55 0.8 0.6

0.5 0.5 0.7 0.3 0.6 0.9 0.7

The Φ value of equation (4) for the nearest neighbor using the data given in the Table I is calculated and is given by:

Φ =0.6948 Therefore, the channels closest and/or greater than the

Φ value will have a better choice of the selection by the

SU. In the above table, the channels 3 and 7 have primary choice and channels 1, 4, 6, and 8 will get second choice for selection. Channel 5 has low priority. In the case of ACF, we will consider the interest of two users on a particular channel and their ratings. In this case we will look into the quality of service (QoS) and ratings on a particular channel by the two users. The interest factor will be calculated using the channel features called QoS and Ratings as shown in Table II. TABLE II CHANNEL RATING BY TWO USERS FOR PREFERENCE

User#

Rating

QoS

χ

1

0.7

0.8

0.9

2

0.8

0.75

0.9

Using the difference formula in equation (5), and the data from Table II, the ∆ value is calculated and is given by:

∆ = 0.0139

Case 2

In the current case, since the difference between the interests of two users is close to 1%, the two users will bid for the channel. The highest bidder wins the channel or highest preference by the priority allocation will get the channel. The preference (priority) may be hand-shaking situation, where a user is moving from one access point to another. Therefore, in the current channel allocation the cooperative games use the economic model for preference and allocation of the channel. The characteristic function is based on CBR or ACF model. 7. SIMULATIONS In this section we will discuss efficient utilization of spectrum by secondary users and at the same time the SU must get the preferred channel. The following algorithm CBR-ACF calculates and assigns the appropriate channel using priorities to SUs at any given time. Algorithm CBR-ACF a) Find available channels (generate randomly) b) Use the nearest neighbor algorithm (CBR) and o find the channel (s) closest to user1 preference o find the channel (s) closest to user 2 preference c)

Using ACF formula find the user preferences for the same available channels between two users d) Assign the channel using CBR and ACF data e) Repeat the steps (a) to (d) for another user The Algorithm CBR-ACF selects the channel closest to the user choice. If more than one user is interested on the same channel then the system must select the preferred user. The simulations were conducted using random data. The program was written in MATLAB. In the current case, we assumed 99 channels. The values for CR, CRR, and w were assigned using a random function. The sim values are calculated for each channel. Many simulations were conducted and recorded for key explanation of algorithm CBR-ACF. Case 1 The following data was obtained using the Algorithm CBR-ACF and equations (4) and (5). Basing the simulations data, we concluded the current available channel will be allocated to the preferred user.

Φ =0.5079 Free channels: 51 8 6 63 62 Preferred channel: 51 Preferred CRR for this channel: 0.5136 ACF for this channel calculated for 3 user cases: User1 ACF = 0.0241 User2 ACF =0.0378 User3 ACF =0.0295 According to this data user 1 will be assigned the channel 51.

Φ =0.4769 Free channels: 71 50 47 6 68 Preferred channel: 6 Preferred CRR for this channel: 0.4218 ACF for this channel calculated for 3 user cases: User1 ACF = 0.0381 User2 ACF =0.0298 User3 ACF =0.0542 According to this data user 2 will be assigned the channel 6. For example, consider the case 2; the CBR assigns the available channel to user 1 with its priorities. But considering priorities of all users and available channels, we calculated the closest matching and assigned the channel with combined decision of CBR and ACF. This decision is the collaborative, since we consider all users’ priorities and recording their suggestions through weights, channel ratings, and priorities. We are working on the reward and penalty depending upon the assignment. We are also working on the bidding policy, when two users are closely matches for request. 8. CONCLUSION Recent developments show that the there are different approaches for the efficient utilization of the spectrum. The approaches include genetic algorithms, neural networks, stochastic models, game models, and economic models. These models are used display the by dynamic spectrum access concept as a catalyst for efficient utilization of unutilized and underutilized spectrum. The channel-gain in an opportunistic and collaborative way is also a part of efficient utilization of the spectrum. In the current research we introduced a new approach using casebased reasoning and automatic collaborative filtering with the cooperative game approach. This combination brings the cooperative game work in selection and gaining of the channel access. The research was presented as a basic game model and channel gain by the SUs. The channel assignment to SUs was done by using the CBR and ACF models. These approaches were demonstrated using examples through a proposed Algorithm CBR-ACF. The future work involves the identification of preferred SUs using reward and punishment model. Furthermore, automatic collection of spectrum holes and prioritizing the SUs using economic and biological models will save time in the fast allocation of channels to SUs. Automatic prioritizing also saves the time and improves the quality of channel assignment (to a preferred and needed user). ACKNOWLEDGEMENT The research work was supported by Air Force Research Laboratory/Clarkson Minority Leaders Program through contract No: FA8650-05-D-1912. The author wishes to express appreciation to Dr. Connie Walton, Provost & Vice President for Academic Affairs, Grambling State University, for her continuous support. REFERENCES

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